Question

A garden is 90 m long and 75 m broad. A path 5m broad is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare. A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65m. Find the area of the path.

Answer 1

Hint:
First, we will find the area of the garden using the formula for area of a rectangle. Then, we will add the width of the path to the length and breadth of the park and find the total area occupied by the path and the garden. Finally, we will subtract the area of the garden from this total area and we will obtain the area of the path.
Formula used: Area of a rectangle is given by \[A = l \times b\] where \[l\] and \[b\] are the length and breadth of the rectangle, respectively.

Complete step by step solution:
We will first draw the figure using the information given in the question.

It is given to us that the length of the garden is 90 m and the breadth is 75 m.
Now we will substitute the length and breadth in the formula and find the area of the garden.
\[A = 90 \times 75 = 6750{\rm{ }}{{\rm{m}}^2}\]
The area of the garden is 6750 \[{{\rm{m}}^2}\].
Let us find the area of the outer rectangle.
The length of the outer rectangle \[ = 90 + 5 = 95{\rm{m}}\].
The breadth of the outer rectangle \[ = 75 + 5 = 80{\rm{m}}\].
Now we will substitute the length and the breadth of the outer rectangle in the formula for area.
\[A = 95 \times 80 = 7600{\rm{ }}{{\rm{m}}^2}\]
The area of the outer triangle is 7600 \[{{\rm{m}}^2}\].
Now, let us find the area of the path.
The area of the path is the difference between the area of the outer rectangle and the area of the garden.
\[{A_{{\rm{path}}}} = 7600 - 6750 = 850{\rm{ }}{{\rm{m}}^2}\]
The area of the path is 850 \[{{\rm{m}}^2}\].
1 hectare is equivalent to 10000 square metres.
Let’s find the area of the path in hectares, for that we will divide the area of the path by 10000.
\[{A_{{\rm{path}}}} = \dfrac{{850}}{{10000}} = 0.085{\rm{ ha}}\]
The area of the path is 0.085 ha.

The length of the park is 125 m and the breadth is 65 m. Let us substitute the length and breadth in the formula and find the area of the park.
\[\begin{array}{l}A = 125 \times 65\\A = 8125{\rm{ }}{{\rm{m}}^2}\end{array}\]
The area of the park is 8125 \[{{\rm{m}}^2}\].
Let us find the area of the outer rectangle.
The length of the outer rectangle will be $125 + 3$ that is $128$ m.
The breadth of the outer rectangle will be $65 + 3$ that is $68$ m.
Let us substitute the length and the breadth in the formula for the area of a rectangle.
\[A = 128 \times 68 = 8704{\rm{ }}{{\rm{m}}^2}\]
Area of the outer triangle is 8704 \[{{\rm{m}}^2}\].
Now, let us find the area of the path.
The area of the path is the difference between the area of the outer rectangle and the area of the park.
\[{A_{{\rm{path}}}} = 8704 - 8125 = 579{\rm{ }}{{\rm{m}}^2}\]

The area of the path is 579 \[{{\rm{m}}^2}\].

Note:
We must remember that 1 metre square equals 0.0001 hectares. If the length or breadth of the rectangle is given in any other unit (say cm), we must convert it into metres or to convert the area into square centimetres. Such problems can also be seen in real life, there is usually a tiled path present outside parks which serves as a boundary for the park.